We address theoretically differences and similarities on the electronic structure of CdSe/CdS dot-in-dot nanocrystals (NCs) with wurtzite/wurtzite (WZ/WZ), zinc-blende/zinc-blende (ZB/ZB) and polytype ZB/WZ crystalline phases, as they are currently being synthesized and used in optoelectronic devices. We show that the electronic structure of polytypic CdSe/CdS NCs closely resembles that of WZ or ZB NCs with regard to quantum confinement and strain, resulting in similar single-exciton wave functions. The main differences arise in the nature and magnitude of built-in electric fields. We predict that these fields are stronger in polytypes than in pure WZ or ZB NCs due to the sharp spontaneous polarization mismatch between the cubic core and the hexagonal shell lattices. Polarization in NCs is currently believed to be screened by several surface effects. In polytypical structures, however, the polarization mismatch at the interface may create effective charges that are sufficiently far from the outer surface to be quenched. To make a definitive assessment on this controversial issue, we propose experiments in polytypic ZB/WZ NCs where both core and shell are made of CdSe. In such a case, band offsets are small, strain is absent, and our calculations predict pyroelectricity should become the driving force, inducing transitions from type-I to type-II excitons with increasing core or shell size. [-]